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User:Jon Awbrey/SCRATCHPAD (view source)

Revision as of 00:06, 2 February 2009

689 bytes added ,  00:06, 2 February 2009
→‎Rule 8
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|- style="height:40px; text-align:center"
 
|- style="height:40px; text-align:center"
 
| width="80%" |  
 
| width="80%" |  
−
| width="20%" style="border-left:1px solid black" | <math>\operatorname{Rule~7}</math>
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| width="20%" style="border-left:1px solid black" | <math>\operatorname{Rule~8}</math>
 
|}
 
|}
 
|-
 
|-
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| width="2%"  style="border-top:1px solid black" | &nbsp;
 
| width="2%"  style="border-top:1px solid black" | &nbsp;
 
| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
 
| width="18%" style="border-top:1px solid black" | <math>\text{If}\!</math>
−
| width="60%" style="border-top:1px solid black" | <math>p, q ~:~ X \to \underline\mathbb{B}</math>
+
| width="60%" style="border-top:1px solid black" | <math>s, t ~\text{are sentences about things in}~ X</math>
 
| width="20%" style="border-top:1px solid black; border-left:1px solid black" | &nbsp;
 
| width="20%" style="border-top:1px solid black; border-left:1px solid black" | &nbsp;
 
|- style="height:40px"
 
|- style="height:40px"
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|- style="height:40px"
 
|- style="height:40px"
 
| width="2%"  style="border-top:1px solid black" | &nbsp;
 
| width="2%"  style="border-top:1px solid black" | &nbsp;
−
| width="18%" style="border-top:1px solid black" | <math>\operatorname{R7a.}</math>
+
| width="18%" style="border-top:1px solid black" | <math>\operatorname{R8a.}</math>
−
| width="60%" style="border-top:1px solid black" | <math>p ~=~ q</math>
+
| width="60%" style="border-top:1px solid black" | <math>s ~\Leftrightarrow~ t</math>
−
| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" | <math>\operatorname{R7a~:~R6a}</math>
+
| width="20%" style="border-top:1px solid black; border-left:1px solid black; text-align:center" |
 +
<math>\operatorname{R8a~:~D7a}</math>
 
|- style="height:20px"
 
|- style="height:20px"
 
| &nbsp;
 
| &nbsp;
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|- style="height:60px"
 
|- style="height:60px"
 
| &nbsp;
 
| &nbsp;
−
| <math>\operatorname{R7b.}</math>
+
| <math>\operatorname{R8b.}</math>
−
| <math>\overset{X}{\underset{x}{\forall}}~ (p(x) ~=~ q(x))</math>
+
| <math>\downharpoonleft s \downharpoonright ~=~ \downharpoonleft t \downharpoonright</math>
−
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R7b~:~R6b}</math>
+
| style="border-left:1px solid black; text-align:center" |
 +
<p><math>\operatorname{R8b~:~D7b}</math></p>
 +
<p><math>\operatorname{R8b~:~R7a}</math></p>
 
|- style="height:20px"
 
|- style="height:20px"
 
| &nbsp;
 
| &nbsp;
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|- style="height:60px"
 
|- style="height:60px"
 
| &nbsp;
 
| &nbsp;
−
| <math>\operatorname{R7c.}</math>
+
| <math>\operatorname{R8c.}</math>
−
| <math>\operatorname{Conj_x^X}~ (p(x) ~=~ q(x))</math>
+
| <math>\overset{X}{\underset{x}{\forall}}~ (\downharpoonleft s \downharpoonright (x) ~=~ \downharpoonleft t \downharpoonright (x))</math>
−
| style="border-left:1px solid black; text-align:center" |
+
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R8c~:~R7b}</math>
−
<p><math>\operatorname{R7c~:~R6c}</math></p>
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|- style="height:20px"
−
<p><math>\operatorname{R7c~:~P1a}</math></p>
+
| &nbsp;
 +
| &nbsp;
 +
| &nbsp;
 +
| style="border-left:1px solid black; text-align:center" | <math>::\!</math>
 +
|- style="height:40px"
 +
| &nbsp;
 +
| <math>\operatorname{R8d.}</math>
 +
| <math>\operatorname{Conj_x^X}~ (\downharpoonleft s \downharpoonright (x) ~=~ \downharpoonleft t \downharpoonright (x))</math>
 +
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R8d~:~R7c}</math>
 
|- style="height:20px"
 
|- style="height:20px"
 
| &nbsp;
 
| &nbsp;
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|- style="height:40px"
 
|- style="height:40px"
 
| &nbsp;
 
| &nbsp;
−
| <math>\operatorname{R7d.}</math>
+
| <math>\operatorname{R8e.}</math>
−
| <math>\operatorname{Conj_x^X}~ (p(x) ~\Leftrightarrow~ q(x))</math>
+
| <math>\operatorname{Conj_x^X}~ (\downharpoonleft s \downharpoonright (x) ~\Leftrightarrow~ \downharpoonleft t \downharpoonright (x))</math>
−
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R7d~:~P1b}</math>
+
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R8e~:~R7d}</math>
 
|- style="height:20px"
 
|- style="height:20px"
 
| &nbsp;
 
| &nbsp;
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|- style="height:60px"
 
|- style="height:60px"
 
| &nbsp;
 
| &nbsp;
−
| <math>\operatorname{R7e.}</math>
+
| <math>\operatorname{R8f.}</math>
−
| <math>\operatorname{Conj_x^X}~ \underline{((}~ p(x) ~,~ q(x) ~\underline{))}</math>
+
| <math>\operatorname{Conj_x^X}~ \underline{((}~ \downharpoonleft s \downharpoonright (x) ~,~ \downharpoonleft t \downharpoonright (x) ~\underline{))}</math>
−
| style="border-left:1px solid black; text-align:center" |
+
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R8f~:~R7e}</math>
−
<p><math>\operatorname{R7e~:~P1c}</math></p>
   
<p><math>\operatorname{R7e~:~$1a}</math></p>
 
<p><math>\operatorname{R7e~:~$1a}</math></p>
 
|- style="height:20px"
 
|- style="height:20px"
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|- style="height:40px"
 
|- style="height:40px"
 
| &nbsp;
 
| &nbsp;
−
| <math>\operatorname{R7f.}</math>
+
| <math>\operatorname{R8g.}</math>
 
| <math>\operatorname{Conj_x^X}~ \underline{((}~ p ~,~ q ~\underline{))}^\$ (x)</math>
 
| <math>\operatorname{Conj_x^X}~ \underline{((}~ p ~,~ q ~\underline{))}^\$ (x)</math>
−
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R7f~:~$1b}</math>
+
| style="border-left:1px solid black; text-align:center" | <math>\operatorname{R8g~:~R7f}</math>
 
|}
 
|}
 
|}
 
|}
Jon Awbrey
12,089

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